Samsung Galaxy Note 3: Broken : Screen, LCD or Digitizer or all?

I am so confused, I've dropped and broken my Note3 but I don't know what and which part I broke.

I've had it in a case and I had an additional screen protector stuck onto it.

At the first glance it doesn't seem broken (resting black screen) but You'd be able to see a cracked corner.

If turned on, The corner will have pixelly black specks, as well as off-coloured purple lines. At the bottom of the screen there'd be a bit of white, purple and other colours. There's random specks and faded smudges of colour on the screen also.

The Display's touch screen works for the most part if I swipe around but I can't select/open/click any of the menu buttons (Additional apps bar etc. )